Diversity maintenance and decision invariance collaborative bearing fault diagnosis method

Abstract

The invention discloses a bearing fault diagnosis method based on cooperation of diversity maintenance and decision invariance, and the method comprises the steps: 1, collecting bearing vibration signals in each health state under different working conditions, and carrying out the fast Fourier transform of the signals, and converting the signals into frequency domain signals, thereby obtaining a data set; 2, constructing a diagnosis model, and training the diagnosis model by using the data set, and 3, processing a frequency domain signal obtained by converting a to-be-detected vibration signal by using the trained diagnosis model, and obtaining a predicted fault diagnosis result; according to the method, rich field related features beneficial to classification are reserved by setting supervision comparison loss, and meanwhile, a uniform and invariant decision function with robustness for the diversified features is learned through flat minimum value alignment loss, so that decision invariance in a real sense is realized.

Description

Technical Field

[0001] This invention belongs to the field of intelligent fault diagnosis technology, and in particular relates to a bearing fault diagnosis method that combines diversity preservation and decision invariance. Background Technology

[0002] Intelligent fault diagnosis technology is a core support for ensuring the safe and reliable operation of modern industrial systems. The operating conditions of industrial equipment are complex and variable, often affected by factors such as load, speed, and temperature; this phenomenon is known as operating condition variation. While deep learning-based diagnostic methods have made significant progress, their performance is highly dependent on a core assumption: that the distributions of training and test data are consistent. However, in practical applications, due to the continuous changes in operating conditions, the distribution of test data (target domain) often deviates from the distribution of training data (source domain), resulting in a domain shift problem.

[0003] Domain bias severely restricts the generalization ability and practical deployment effectiveness of existing intelligent diagnostic models. A model trained under existing operating conditions may experience a sharp drop in diagnostic accuracy when faced with data from unknown operating conditions. To address this issue, domain generalization techniques have emerged. Their goal is to learn a unified and robust model from multiple known source domains (various operating conditions), enabling it to be directly applied to unknown target domains without requiring retraining with any target domain data.

[0004] Current domain generalization methods primarily employ two contradictory technical approaches: one is invariant feature learning, whose core idea is to eliminate feature differences between different domains and learn a domain-invariant common feature space. However, while eliminating domain-related variations, this approach may also lose valuable, domain-specific, subtle feature information beneficial for fault classification, leading to feature collapse and performance bottlenecks. The other approach is feature diversity preservation, which advocates preserving or even enhancing domain-specific feature variations, arguing that these variations provide the model with richer information to cope with unknown environments. However, this approach lacks an effective mechanism to learn a unified decision logic and is susceptible to interference from spurious correlations between domains. Therefore, how to learn a cross-domain, universal, and invariant decision function while preserving beneficial feature diversity has become a key challenge that current domain-generalized intelligent fault diagnosis technologies urgently need to overcome. Summary of the Invention

[0005] The purpose of this invention is to provide a bearing fault diagnosis method that combines diversity preservation with decision invariance, in order to solve the problem that the diagnostic model has insufficient generalization ability due to domain bias, and that the two existing generalization methods cannot learn a cross-domain universal and invariant decision function while preserving beneficial feature diversity.

[0006] This invention adopts the following technical solution: a bearing fault diagnosis method that synergizes diversity preservation and decision invariance, comprising:

[0007] Step 1: Collect bearing vibration signals under different working conditions and health states, and convert them into frequency domain signals by fast Fourier transform to obtain a dataset;

[0008] Step 2: Construct a diagnostic model and train it using the dataset. When training the diagnostic model, the model is trained using the empirical risk minimization loss for basic fault classification, the supervised contrastive loss for preserving cross-domain feature diversity, and the flat minimum alignment loss for learning cross-domain invariant decision functions. The diagnostic model includes a shared feature extractor and a unified classifier.

[0009] Step 3: Use the trained diagnostic model to process the frequency domain signal obtained by converting the vibration signal under test, and obtain the predicted fault diagnosis result.

[0010] The beneficial effects of this invention are:

[0011] This invention retains rich, classification-friendly domain-related features by setting a supervised contrast loss, and learns a unified and invariant decision function that is robust to these diverse features through a flat minimum alignment loss, thus achieving true decision invariance. This invention fundamentally solves the core contradiction in domain generalization, thereby significantly improving the generalization ability and diagnostic accuracy of the diagnostic model under unknown conditions. Attached Figure Description

[0012] Figure 1 This is a flowchart of the present invention;

[0013] Figure 2 Test diagrams for generating test benches based on bearing data in embodiments of the present invention;

[0014] Figure 3 This is a loss landscape diagram of an embodiment of the present invention across three training domains. Detailed Implementation

[0015] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0016] This invention discloses a bearing fault diagnosis method that synergistically preserves diversity and ensures decision invariance, specifically comprising three steps, as follows: Figure 1 As shown.

[0017] Step 1: Collect bearing vibration signals under different working conditions and health states, and convert them into frequency domain signals by fast Fourier transform to obtain a dataset.

[0018] First, bearing vibration signals under different operating conditions and at various health states were collected. The original one-dimensional vibration signals were divided into 1024-bit samples, and a Fast Fourier Transform was performed on each sample to convert it from the time domain to the frequency domain. The amplitude spectrum of the frequency domain signal was then reconstructed into a 32*32 two-dimensional format and used as the input to the model. Data under different operating conditions were defined as different domains, and the entire dataset was divided into multiple source domain data and one target domain data. All source domain data were labeled according to their health status.

[0019] Step 2: Construct a diagnostic model and train it using the dataset. When training the diagnostic model, the model is trained using the empirical risk minimization loss for basic fault classification, the supervised contrastive loss that preserves cross-domain feature diversity, and the flat minimum alignment loss that learns cross-domain invariant decision functions. The diagnostic model includes a shared feature extractor and a unified classifier.

[0020] A diagnostic model consisting of a shared feature extractor and a unified classifier is constructed. The model parameters are optimized through iterative training on source domain data. This training process is achieved by optimizing a combined loss function, which synergistically combines a supervised contrastive loss to preserve cross-domain feature diversity and a flat minimum alignment loss to learn cross-domain invariant decision functions.

[0021] To preserve beneficial and unique feature information within each domain and prevent feature collapse caused by the pursuit of invariance, this invention introduces supervised contrastive loss. Its core lies in organizing samples in the feature space through a specific positive-negative sample pair definition strategy: for any anchor sample i in the training data, its positive sample set P(i) is defined as other samples sharing the same class label and source domain as that anchor sample; all other samples, including samples of the same class from different domains, are defined as negative samples. This is achieved by minimizing the supervised contrastive loss L... SCL The model is guided to bring samples of the same domain and type closer together while pushing away samples of different domains or different classes, thus maintaining rich feature diversity.

[0022] Supervised comparison loss L SCL The formula is expressed as:

[0023]

[0024] Where i is the set of indices of samples within a mini-batch, i∈I represents the index of the currently selected anchor sample; A(i)=I\{i} is the set of indices of all samples except the anchor sample; a is the index used to traverse the set to calculate the denominator; P(i) is the set of positive sample indices, containing the indexes p of all samples with the same class and source domain as the anchor sample, |P(i)| is the cardinality of P(i); zi ,z p ,z a These are the L2-normalized feature representations of anchor samples, positive samples, and arbitrary samples, respectively; z i ·z a τ represents the dot product of eigenvectors. c This refers to temperature hyperparameters.

[0025] To learn a uniform decision function robust to all source domains while preserving feature diversity, this invention introduces a flat minimum alignment loss, aiming to approximate an ideal goal of finding the intersection of the parameter sets of the optimal classifiers for all source domains. This approximate achievement is accomplished by finding and aligning "flat minimum regions" in the loss landscape of each source domain.

[0026] The construction of the flat minimum alignment loss aims to approximate an ideal objective, which is to find a classifier parameter φ. * This ensures that the parameter satisfies optimality across all source domains, meaning that the parameter lies within the set of optimal classifier parameters for all individual source domains. In the intersection of the two, it is defined as:

[0027] in

[0028] Where S is the total number of source domains; θ and φ are the parameters of the feature extractor and classifier, respectively; R s This refers to the risks in the source domain s.

[0029] The core challenge of the above formula lies in the unavailability of the optimal set mentioned above. The optimal parameter set corresponding to each domain. It is a discrete, abstract entity that cannot be directly solved through computation. Furthermore, under the constraint of explicit feature diversity, the intersection of such "optimal parameter points" may not even exist.

[0030] To overcome this technical bottleneck, this invention proposes a computable approximation scheme. Inspired by the correlation between the minimum flat loss and model robustness, this invention assumes that any parameter vector within a flat low-loss region can be considered a robust near-optimal solution. Therefore, this invention uses the flat loss region corresponding to the optimal set to approximate the optimal parameter set that cannot be directly solved.

[0031] Define a flat region ρ in a specific domain: For any domain s and radius ρ > 0, a region ρ is flat. Defined as the set of parameters for a robust near-optimal classifier, its mathematical expression is:

[0032]

[0033] Among them, C s (θ)=min φ′ R s (θ,φ′)+δ represents the risk threshold for the flat region, where δ is a minimal tolerance hyperparameter. This set... It can serve as the ideal optimal parameter set. A practical alternative.

[0034] Based on the above approximation, the optimization objective is transformed into finding a satisfying... The parameter solution is obtained. However, even so, the intersection of the regions may still be an empty set. To address this, this rigid set membership constraint is relaxed into a penalty term for "violation of membership conditions," and a continuously optimizable objective function is constructed.

[0035] Definition of violation degree: The parameter vector φ violates the flat region. The degree of membership can be quantified by the following formula:

[0036]

[0037] By definition, if and only if the degree of violation When the parameter φ belongs to the flat region, that is

[0038] To satisfy the region intersection constraint, the violation degree of all regions must be 0 simultaneously, from which the following proposition can be derived.

[0039] Proposition 1 (Equivalence of intersection constraints and minimum-maximum violation): Due to the violation degree It has nonnegativity, therefore the condition Mathematically, this is equivalent to the maximum violation degree of all domains being 0, that is:

[0040]

[0041] This equivalence relation shows that the most robust way to achieve intersection constraints is to minimize the worst-case violation in all domains.

[0042] Therefore, in the intersection of regions The problem of finding a feasible solution can be relaxed into a minimax optimization problem.

[0043] Threshold term C in the formula s While (θ) is crucial to the definition of the set, it exists only as an additive constant in the optimization process for φ. Therefore, optimizing the minimum-maximum violation is equivalent to optimizing the simplified objective that removes this constant term, from which the FMA-IRM regularization term can be directly derived:

[0044]

[0045] Where s is the source domain index, S is the total number of source domains; R s Let be the risk in the source domain s; θ and φ are the parameters of the feature extractor and classifier, respectively; ∈ is the perturbation vector applied to the parameter φ; and ρ is the preset neighborhood radius.

[0046] The above can be interpreted as follows: when the worst-case risk value exceeds the risk threshold, the state is judged to have violated the local risk flatness condition, and a penalty signal is generated based on this. This signal drives the classifier parameter φ to be updated towards the region that satisfies all source domain conditions during the iterative training of the model.

[0047] The penalty signal is obtained by minimizing the flat minimum alignment loss L. FMA-IRM This is achieved by finding and minimizing the penalty for the most severe violation of the condition in all source domains, thereby simultaneously satisfying the flatness requirement of all domains.

[0048] Using the combined loss function L total The entire diagnostic model is trained end-to-end, and the combined loss function is the standard empirical risk minimization loss L. ERM Supervisory comparison loss L SCL And the minimum alignment loss L FMA-IRM The weighted summation is used to construct the formula.

[0049] The formula for calculating the total training loss is:

[0050] L total =L ERM +λ SCL ·L SCL +λ FMA-IRM ·L FMA-IRM

[0051] Where, λ SCL and λ FMA-IRM To balance the hyperparameters of the various losses, a well-trained shared feature extractor and unified classifier are obtained by minimizing the combined loss function.

[0052] Step 3: Use the trained diagnostic model to process the frequency domain signal obtained by converting the vibration signal under test, and obtain the predicted fault diagnosis result.

[0053] The vibration signal of the bearing under test from the unknown working condition is converted into a frequency domain signal and then input into the trained shared feature extractor and unified classifier to directly obtain the final fault diagnosis result.

[0054] This invention preserves rich, classification-friendly domain-relevant features through supervised contrastive loss, while simultaneously learning a robust, unified, and invariant decision function for these diverse features through flat minimum alignment loss, achieving true decision invariance. This collaborative design fundamentally resolves the core contradiction in domain generalization, thereby significantly improving the diagnostic model's generalization ability and diagnostic accuracy under unknown conditions.

[0055] Example

[0056] This embodiment uses the bearing dataset from Soochow University for experimental verification, such as... Figure 2 As shown in the figure, the dataset contains vibration signals collected under four different radial loads (0 N, 1 kN, 2 kN, 3 kN) at a constant rotational speed. These four conditions are considered as four independent domains. The dataset covers the normal state as well as nine different types and degrees of faults on the inner ring, outer ring, and rolling elements, totaling ten health conditions. Table 1 shows the health condition labels for the bearing dataset.

[0057] Table 1: Health Status Labels of the Bearing Dataset

[0058] health status Fault size / mm Category Tags Training samples Test samples Symbolic representation Inner ring fault 0.2 0 200 200 IF2 Roller failure 0.2 1 200 200 BF2 Outer ring fault 0.2 2 200 200 OF2 Inner ring fault 0.4 3 200 200 IF4 Roller failure 0.4 4 200 200 BF4 Outer ring fault 0.4 5 200 200 OF4 Inner ring fault 0.6 6 200 200 IF6 Roller failure 0.6 7 200 200 BF6 Outer ring fault 0.6 8 200 200 OF6 normal \ 9 200 200 NO

[0059] In each experiment, one work condition domain was selected as the unknown target domain for testing, while the other three work condition domains were used as source domains for training. Table 2 shows the specific task partitioning based on the SDUST dataset.

[0060] Table 2 Diagnostic Task Division

[0061] Task ID source domain target domain T1 1kN, 2kN, 3kN 0kN T2 0kN, 2kN, 3kN 1kN T3 0kN, 1kN, 3kN 2kN T4 0kN, 1kN, 2kN 3kN

[0062] All comparison methods and the method in this embodiment use ResNet-18 as the shared feature extractor, followed by a fully connected layer as the classifier. Network structure parameters and training hyperparameters are kept consistent to ensure fair comparison. The main parameter settings for the method in this embodiment are shown in Table 3.

[0063] Table 3 Main Parameter Settings

[0064] parameter Optimizer Learning rate Batch Size Training rounds <![CDATA[λ SCL ]]> <![CDATA[λ FMA-IRM ]]> value SGD 1e-3 128 100 1 1

[0065] To verify the superiority of the method in this embodiment, representative methods from various generalization fields were selected for comparison, as detailed in Table 4.

[0066] Table 4 Comparison of test accuracy between the method in this embodiment and the comparative method.

[0067]

[0068]

[0069] The origins of each English letter in Table 4 are as follows:

[0070] ERM originates from VAPNIK V N. Principles of risk minimization for learning theory[J]. Advances in Neural Information Processing Systems, 1992, 4: 831-838. The core idea of ​​ERM is to minimize the average risk across all source domains.

[0071] SAM originates from FORET P, KLEINER A, MOBAHI H, et al. Sharpness-aware minimization for efficiently improving generalization [R]. arXiv preprint arXiv:2010.01412,2020. The core idea of ​​SAM is to minimize the perceived sharpness and find a flat loss region.

[0072] CORAL originates from SUN B, SAENKO K. Deep coral: Correlation alignment for deepdomain adaptation[C] / / European Conference on Computer Vision.Springer,2016:443-450. The core idea of ​​CORAL is to align the second-order statistics (covariance) of features from different domains.

[0073] MMD originates from LONG M, CAO Y, WANG J, et al. Learning transferable features with deep adaptation networks[C] / / Proceedings of the 32nd International Conference on Machine Learning.2015:97-105. The core idea of ​​MMD is to minimize the feature distribution distance in the reproducing kernel Hilbert space.

[0074] DANN originates from GANIN Y, LEMPITSKY V. Unsupervised domain adaptation by backpropagation[C] / / Proceedings of the 32nd International Conference on Machine Learning.2015:1180-1189. The core idea of ​​DANN is to learn domain-invariant features by using domain adversarial training.

[0075] Mixup originates from ZHANG H, CISSE M, DAUPHIN YN, et al. mixup: Beyond empirical risk minimization [R]. arXiv preprint arXiv:1710.09412,2017. The core idea of ​​Mixup is to create synthetic data by linearly interpolating samples.

[0076] MixStyle originates from ZHOU K, YANG Y, QIAO Y, et al. Domain generalization with mixstyle[R].arXiv preprint arXiv:2104.02008,2021. The core idea of ​​MixStyle is to mix feature statistics between instances.

[0077] IMLNet, GUAN W, WANG S, CHEN Z, et al. Domain generalization network based on inter-domain multivariate linearization for intelligent fault diagnosis[J]. Reliability Engineering & System Safety, 2025, 261: 111055., The core idea of ​​IMLNet is to enhance generalization ability by constructing new domains through linear fusion.

[0078] DGNIS originates from ZHAO C, SHEN WA, domain generalization network combing invariance and specificity towards real-time intelligent fault diagnosis[J].Mechanical Systems and Signal Processing,2022,173:108990. The core idea of ​​DGNIS is invariant features + domain-specific classifier.

[0079] Table 4 summarizes the diagnostic accuracy of this embodiment and the nine comparative methods. As can be seen from Table 4, the average accuracy of ERM is 95.91%, indicating that simply minimizing the average risk across all source domains has limited performance when facing the domain shift problem. Compared to ERM, CORAL (95.31%) and DANN (95.55%) did not show a stable performance advantage, suggesting that strategies such as forcibly aligning feature distributions and eliminating domain differences may lead to the loss of discriminative information beneficial to classification, thus limiting the model's generalization ability. On the other hand, MixStyle (94.83%) even performed worse than the baseline, indicating that simply increasing feature variations without a unified decision learning mechanism is unreliable.

[0080] In comparison, the method in this embodiment performs exceptionally well across all diagnostic tasks, achieving an average accuracy of 98.07%. This represents a 0.51% improvement in accuracy compared to the second-best performing high-performance method, IMLNet (97.56%), and a significant 2.16% improvement compared to ERM. This superiority stems from the unique collaborative design of this embodiment. On one hand, supervised contrastive learning effectively preserves the diversity of structured features crucial for classification, avoiding information loss. On the other hand, it introduces a robust decision learning mechanism, ensuring that the model can learn a unified and invariant classification logic across diverse features. The synergistic effect of these two components allows the model to fully utilize unique information from various domains while forming a common decision criterion with strong generalization ability, resulting in a performance gain greater than the sum of its parts (1+1>2).

[0081] Figure 3 This is a visual comparison of the classifier loss landscape learned by the method of this embodiment under task T1 for three source domains (1kN, 2kN, 3kN). Figure 3As can be seen, near the finally converged model parameters (marked with an asterisk "☆" in the figure), the log loss of the model changes across each independent source domain when the classifier parameters undergo small perturbations in the two main directions α and β. The lighter-colored areas in the figure represent flat regions with low loss values, while the darker-colored areas represent steep regions with high loss values. From... Figure 3 As can be clearly observed, despite the differences in data distribution across the three source domains (1kN, 2kN, 3kN), the method in this embodiment successfully found a shared, common low-loss flat region for all source domains. Specifically, the flat regions in the three subgraphs exhibit highly consistent positions and shapes in the parameter space, indicating that the model has found a solution space robust to all source domains. The final convergence point (marked with an asterisk "☆") precisely falls at the center of this common flat region, visually validating the effectiveness of the flat minimum alignment mechanism in this embodiment. This result demonstrates that the method in this embodiment does not simply compromise among multiple loss functions, but actively reshapes and aligns the loss landscape across different domains, thereby learning a truly generalizable and invariant decision function.

[0082] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A bearing fault diagnosis method that synergizes diversity preservation and decision invariance, characterized in that, include: Step 1: Collect bearing vibration signals under different working conditions and health states, and convert them into frequency domain signals by fast Fourier transform to obtain a dataset; Step 2: Construct a diagnostic model and train it using the dataset. When training the diagnostic model, the model is trained using the empirical risk minimization loss for basic fault classification, the supervised contrastive loss for preserving cross-domain feature diversity, and the flat minimum alignment loss for learning cross-domain invariant decision functions. The diagnostic model includes a shared feature extractor and a unified classifier. Step 3: Use the trained diagnostic model to process the frequency domain signal obtained by converting the vibration signal under test, and obtain the predicted fault diagnosis result.

2. The bearing fault diagnosis method according to claim 1, characterized in that, This is achieved by optimizing the combined loss function during the training of the diagnostic model. The combined loss function is as follows: L total =L ERM +λ SCL ·L SCL +λ FMA-IRM ·L FMA-IRM Where, λ SCL and λ FMA-IRM These are the hyperparameters that balance the various losses, L total For the combined loss function, L SCL To monitor and compare losses, L FMA-IRM The minimum alignment loss is for flatness.

3. The bearing fault diagnosis method according to claim 2, which combines diversity preservation and decision invariance, is characterized in that... The formula for the supervised comparison loss is expressed as: Where i is the set of indices of samples within a mini-batch, i∈I represents the index of the currently selected anchor sample; A(i)=I\{i} is the set of indices of all samples except the anchor sample; a is the index used to traverse the set to calculate the denominator; P(i) is the set of positive sample indices, containing the indexes p of all samples with the same class and source domain as the anchor sample, |P(i)| is the cardinality of P(i); z i ,z p ,z a These are the L2-normalized feature representations of anchor samples, positive samples, and arbitrary samples, respectively; z i ·z a τ represents the dot product of eigenvectors. c This refers to temperature hyperparameters.

4. The bearing fault diagnosis method according to claim 2, characterized in that, The method for constructing the flat minimum alignment loss function is as follows: For each source domain s, the worst-case risk of the current classifier parameter φ in a neighborhood is calculated by applying an L2 norm perturbation vector ∈ with a preset radius ρ as the upper limit. This risk value is given by the following formula: The worst-case risk value is compared with a preset, domain-dependent risk threshold C. s (θ) is compared, where the risk threshold is defined as the minimum risk value of the current domain s under all possible classifier parameters plus a small tolerance δ, i.e.: C s (θ)=min φ′ R s (θ,φ′)+δ When the worst-case risk value exceeds the risk threshold, the state is determined to violate the local risk flatness condition, and a penalty signal is generated based on this. This signal drives the classifier parameter φ to be updated to the region that satisfies all source domain conditions during the iterative training of the model. The penalty signal is obtained by minimizing the flat minimum alignment loss L. FMA-IRM This is achieved through [the means].

5. The bearing fault diagnosis method according to claim 4, characterized in that, The flat minimum alignment loss L FMA-IRM The formula is expressed as: Among them, R s Let be the risk in the source domain s; θ and φ are the parameters of the shared feature extractor and the unified classifier, respectively; ε is the perturbation vector applied to parameter φ; and ρ is the preset neighborhood radius.

Images